Basic Math Examples

$\frac{1}{2} - \frac{1^{3}}{3} - (- \frac{1^{3}}{3} - (- 1))$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{1}{2} \cdot \frac{3}{3} - \frac{1^{3}}{3} - (- \frac{1^{3}}{3} - (- 1))$

Step 1.2

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{3}{2 \cdot 3} - \frac{1^{3}}{3} - (- \frac{1^{3}}{3} - (- 1))$

Step 1.3

Multiply $\frac{1^{3}}{3}$ by $\frac{2}{2}$ .

$\frac{3}{2 \cdot 3} - (\frac{1^{3}}{3} \cdot \frac{2}{2}) - (- \frac{1^{3}}{3} - (- 1))$

Step 1.4

Multiply $\frac{1^{3}}{3}$ by $\frac{2}{2}$ .

$\frac{3}{2 \cdot 3} - \frac{1^{3} \cdot 2}{3 \cdot 2} - (- \frac{1^{3}}{3} - (- 1))$

Step 1.5

Write $- (- \frac{1^{3}}{3} - (- 1))$ as a fraction with denominator $1$ .

$\frac{3}{2 \cdot 3} - \frac{1^{3} \cdot 2}{3 \cdot 2} + \frac{- (- \frac{1^{3}}{3} - (- 1))}{1}$

Step 1.6

Multiply $\frac{- (- \frac{1^{3}}{3} - (- 1))}{1}$ by $\frac{6}{6}$ .

$\frac{3}{2 \cdot 3} - \frac{1^{3} \cdot 2}{3 \cdot 2} + \frac{- (- \frac{1^{3}}{3} - (- 1))}{1} \cdot \frac{6}{6}$

Step 1.7

Multiply $\frac{- (- \frac{1^{3}}{3} - (- 1))}{1}$ by $\frac{6}{6}$ .

$\frac{3}{2 \cdot 3} - \frac{1^{3} \cdot 2}{3 \cdot 2} + \frac{- (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 1.8

Multiply $2$ by $3$ .

$\frac{3}{6} - \frac{1^{3} \cdot 2}{3 \cdot 2} + \frac{- (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 1.9

Reorder the factors of $3 \cdot 2$ .

$\frac{3}{6} - \frac{1^{3} \cdot 2}{2 \cdot 3} + \frac{- (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 1.10

Multiply $2$ by $3$ .

$\frac{3}{6} - \frac{1^{3} \cdot 2}{6} + \frac{- (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 - 1^{3} \cdot 2 - (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 3

Simplify each term.

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Step 3.1

One to any power is one.

$\frac{3 - 1 \cdot 1 \cdot 2 - (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 3.2

Multiply $- 1 \cdot 1 \cdot 2$ .

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Step 3.2.1

Multiply $- 1$ by $1$ .

$\frac{3 - 1 \cdot 2 - (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 3.2.2

Multiply $- 1$ by $2$ .

$\frac{3 - 2 - (- \frac{1^{3}}{3} - (- 1)) \cdot 6}{6}$

Step 3.3

Simplify each term.

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Step 3.3.1

One to any power is one.

$\frac{3 - 2 - (- \frac{1}{3} - (- 1)) \cdot 6}{6}$

Step 3.3.2

Multiply $- 1$ by $- 1$ .

$\frac{3 - 2 - (- \frac{1}{3} + 1) \cdot 6}{6}$

Step 3.4

Write $1$ as a fraction with a common denominator.

$\frac{3 - 2 - (- \frac{1}{3} + \frac{3}{3}) \cdot 6}{6}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{3 - 2 - \frac{- 1 + 3}{3} \cdot 6}{6}$

Step 3.6

Add $- 1$ and $3$ .

$\frac{3 - 2 - \frac{2}{3} \cdot 6}{6}$

Step 3.7

Cancel the common factor of $3$ .

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Step 3.7.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{3 - 2 + \frac{- 2}{3} \cdot 6}{6}$

Step 3.7.2

Factor $3$ out of $6$ .

$\frac{3 - 2 + \frac{- 2}{3} \cdot (3 (2))}{6}$

Step 3.7.3

Cancel the common factor.

$\frac{3 - 2 + \frac{- 2}{3} \cdot (3 \cdot 2)}{6}$

Step 3.7.4

Rewrite the expression.

$\frac{3 - 2 - 2 \cdot 2}{6}$

Step 3.8

Multiply $- 2$ by $2$ .

$\frac{3 - 2 - 4}{6}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $2$ from $3$ .

$\frac{1 - 4}{6}$

Step 4.2

Subtract $4$ from $1$ .

$\frac{- 3}{6}$

Step 4.3

Cancel the common factor of $- 3$ and $6$ .

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Step 4.3.1

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{6}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $3$ out of $6$ .

$\frac{3 \cdot - 1}{3 \cdot 2}$

Step 4.3.2.2

Cancel the common factor.

$\frac{3 \cdot - 1}{3 \cdot 2}$

Step 4.3.2.3

Rewrite the expression.

$\frac{- 1}{2}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$